5.7.1: What Is “Free” About Gibbs Free Energy?

We use ΔG or ΔGo to describe many systems (and especially biological ones) because both the magnitude and sign tell us a lot about how that system behaves. We use ΔG (the Gibbs free energy change) rather than ΔH (the enthalpy change) because ΔG tells us how much energy is actually available to bring about further change (or to do work). In any change some of the energy is lost to the environment as the entropy increases, this dissipated energy cannot be used to do any kind of work and is effectively lost. ΔG differentiates the energy produced from the change from the energy that is lost to the surroundings as increased entropy. As an example, when wood is burned, it is theoretically impossible to use all of the heat released to do work; some of the energy goes to increase the entropy of the system. For any change in the system, some of the energy is always lost in this way to the surroundings. This is why it is impossible to build a machine that is 100% efficient in converting energy from one kind to another (although many have tried–Google “perpetual motion machines” if you don't believe us). So the term “free energy” doesn’t mean that it is literally free, but rather that it is potentially available to use for further transformations.

When ΔG is negative, we know that the reaction will be thermodynamically favored.¹⁰⁹ The best-case scenario is when ΔH is negative (an exothermic change in which the system is losing energy to the surroundings and becoming more stable), and ΔS is positive (the system is increasing in entropy). Because T is always greater than 0 (in Kelvins), TΔS is also positive and when we subtract this value from ΔH, we get an even larger negative ΔG value. A good example of such a process is the reaction (combustion) of sugar (C6H12O6) with molecular oxygen (O2):

C6H12O6(s) + 6 O2(g) → 6 CO2(g) + 6 H2O(g).

This is an exothermic process and, as you can see from the reaction equation, it results in the production of more molecules than we started with (often a sign that entropy has increased, particularly if the molecules are of a gas).

A process such as this (-ΔH and +ΔS) is thermodynamically favored at all temperatures. On the other hand, an endothermic process (+ΔH) and a decrease in entropy (-ΔS) will never occur as an isolated reaction (but in the real world few reactions are actually isolated from the rest of the universe). For example, a reaction that combined CO2 and H2O to form sugar (the reverse reaction to the combustion reaction above) is never thermodynamically favored because ΔH is positive and ΔS is negative, making ΔG positive at all temperatures. Now you may again find yourself shaking your head. Everyone knows that the formation of sugars from carbon dioxide and water goes on all over the world right now (in plants)! The key here is that plants use energy from the sun, so the reaction is actually:

captured energy + 6 CO2(g) + 6 H2O(g) ⇆ C6H12O6(s) + 6 O2(g) + excess energy.

Just because a process is thermodynamically unfavorable doesn’t mean that it can never occur. What it does mean is that that process cannot occur in isolation; it must be “coupled” to other reactions or processes.

References

¹⁰⁹ Many people use the term spontaneous, but this is misleading because it could make people think that the reaction happens right away. In fact, ΔG tells us nothing about when the process will happen, only that it is thermodynamically favored. As we will see later, the rate at which a process occurs is governed by other factors.